OFFSET
0,2
COMMENTS
Definition: sigma(n,k) = sigma_k(n) = Sum_{d|n} d^k.
FORMULA
a(n) = Sum_{d|n} (1+d)^n for n>0 with a(0)=1.
a(n) ~ exp(1) * n^n. - Vaclav Kotesovec, Oct 08 2016
MATHEMATICA
Flatten[{1, Table[Sum[Binomial[n, k] * DivisorSigma[k, n], {k, 0, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 08 2016 *)
a[n_] := DivisorSum[n, (1+#)^n &]; a[0] = 1; Array[a, 18, 0] (* Amiram Eldar, Aug 29 2023 *)
PROG
(PARI) {a(n)=if(n==0, 1, sumdiv(n, d, (1+d)^n))}
(PARI) {a(n)=if(n==0, 1, sum(k=0, n, binomial(n, k)*sigma(n, k)))}
(Python)
from sympy import divisors
def A163190(n): return sum((1+d)**n for d in divisors(n, generator=True)) if n else 1 # Chai Wah Wu, Nov 21 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 22 2009
STATUS
approved